Loss vs Magnetization Threshold Phenomenon for Lorentz Nonreciprocity Induced by a Gyrotropic Particle Inside a Cavity

When a plasmonic particle is subject to a static magnetic field, ${B}_{\rm dc}=B_{0} \hat{z}$, its gyrotropic response gives rise to nonreciprocal dynamics of the entire ambient surroundings. This dynamics depends on the particle's excitation which in turn depends on the gyrotropic material damping rate $\Gamma$. Thus intuitively speaking, the heavier the gyrotropic material loss, the weaker the non-reciprocal response. This is indeed the case when the particle is located in free space. In this letter, we quantify nonreciprocity using the defined measure $\cal{R}$ and show that when the gyrotropic particle is placed inside a cavity, the nonreciprocity measure $\cal{R}$ is robust against material loss up to a certain loss threshold, $\Gamma_{th}$ that depends on the magnetic biasing $B_0$